Distributed hypothesis testing under privacy constraints

Abstract

Hypothesis Testing (HT) is one of the central topics of study in statistics. Traditionally, it is assumed that the data on which the hypothesis test is to be performed is available unaltered to the decision maker or detector that performs the hypothesis test. However, this is seldom observed in practice, and often the data is observed remotely, and needs to be communicated to the detector over a noisy communication channel, such as a wired or a wireless communication network. The performance of a hypothesis test obviously depends on how accurately the observed data is communicated to the detector, i.e., less distortion of the data implies better performance. However, in many situations less distortion also implies reduced privacy (security) for the observer as there is the threat of leaking sensitive information to the detector (external eavesdropper). The privacy (security) threat is increasingly becoming an important concern due to the availability of affordable large scale computing resources. In this dissertation, we study HT in a distributed setting, in which the data is observed at a remote node, referred to as observer, and communicated over a noisy channel to the detector, which has access to its own correlated side-information. Considering a hypothesis test on the joint distribution of the observer’s data and detector’s side information, we first study the optimal trade-off between the type I and type II error-exponents, i.e., the trade-off between the asymptotic exponential rate of decay of the type I and type II error probabilities with respect to the number of observed data samples, and establish single-letter inner bounds on this trade-off. Of special interest is the asymmetric case of characterizing the optimal type II error-exponent for a fixed non-zero constraint on the type I error probability, for which we obtain exact single-letter characterization in some special cases. We also investigate the aspects of data privacy in the above setting with a rate-limited noiseless channel by exploring the trade-off between rate, type II error-exponent and privacy. Finally, considering an eavesdropper with access to correlated side-information, we study the trade-off between rate, type II error-exponent and security when the detector and eavesdropper are connected to the observer via a noisy broadcast channel.